Another variational lower bound is based on the \(f\) -divergence representation introduced in [1]} (also referred to as \(f\) -MINE in [2]})
\(I(X;Y) \ge & I_{NWJ}(X;Y) \nonumber \\= & \sup _{\theta \in \Theta } \mathbb {E}_{(\mathbf {x},\mathbf {y})\sim p_{XY}(\mathbf {x},\mathbf {y})}[T_{\theta }(\mathbf {x},\mathbf {y})] \nonumber \\& -\mathbb {E}_{(\mathbf {x},\mathbf {y})\sim p_X(\mathbf {x}) p_Y(\mathbf {y})}[e^{T_{\theta }(\mathbf {x},\mathbf {y})-1}].\) 
